The 400 Series cameras work with any Intel or ARM CPU. The Pi Zero W apparently uses a 1 Ghz ARM 11 Broadcom CPU, so you should be okay on that front.
The Zero W has a USB OTG (On The Go) micro USB port. OTG is designed to allow full-size USB devices to attach to a small device via an adapter. The 400 Series cameras can work with OTG-equipped devices, though there has typically been a higher risk of instability due to insufficient power being supplied to the camera by the OTG port. Examples of single-board computing devices that this issue has been seen on are the Up Board and the Intel Compute Stick.
Intel's guide to setting up the camera on a Raspberry Pi 3 Model B can give an overview of some of the issues involved in a Pi setup with the 400 Series camera.
https://github.com/IntelRealSense/librealsense/blob/master/doc/RaspberryPi3.md
